We can use the qr factorization to get a

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Unformatted text preview: he diagonal Proof. If B = A∗ A, apply QR Factorization to A: B = A∗ A = (QR)∗ (QR) = R∗ Q∗ QR = R∗ IR = R∗ R Letting L = R∗ yields the desired result. We can use the QR Factorization to get a triangularization algorithm. However, we note A = QR is asymmetric, whereas Schur wants A = U ∗ T U . 2.5.9 Proposition. Let A ∈ Mn . Choose A0 = A = Q0 R0 . Next, let An+1 = Rn Qn = Qn+1 Rn+1 , with Qn , Rn chosen as described above for any n ∈ N, then each An is unitarily equivalent t...
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This note was uploaded on 01/16/2014 for the course MATH 6304 taught by Professor Bernhardbodmann during the Fall '12 term at University of Houston.

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